Solving the case with Knox's Decalogue
Judging by chapter 1, this story certainly appears to be a mystery, and many readers seem to think it's a solvable one. If this story is indeed solvable by us, then I submit that it must follow Knox's Decalogue of fair play detective stories. With these commandments, the reader is free from unfair tricks and twists.
For those unfamiliar with the rules, I shall post a modern interpretation of them.
The Knox Decalogue: Umineko version
Knox's 1st: It is forbidden for the culprit to be anyone not mentioned in the early part of the story. (someone from part 1 is the killer. Doesn't need to have a speaking part, and it may even just be part of the background info cards, but we have definitely seen him by now in some form)
Knox's 2nd: It is forbidden for supernatural agencies to be employed as a detective technique. (While this world is undeniably magical there is still no 'I win' button by asking, for instance, a magic mirror to show the location, or identity, of the murderer. The detective, and the detective alone, will solve the case.)
Knox's 3rd: It is forbidden for hidden passages to exist. (no impossible crimes where the only solution is to have the killer pop through a wall wall or teleport into a closed room, also called a locked room mystery, and then sneak away with no traces left behind. Yes, there is magic but that magic is not going to bypass logic, when investigating. All tricks will be discovered during the course of the investigation)
Knox's 4th: It is forbidden for unknown drugs or hard to understand scientific devices to be used. (people can't be killed with some method that is impossible to the reader's viewpoint. Proper explanations are needed for all esoteric murder methods before the case can be resolved)
Knox's 5th: It is forbidden for stereotypical minorities to assist or hinder the detective beyond providing their own conclusions and interpretations, or for said minorities to be the culprit. (having some random butler, or some stereotyped minority, do it is boring and cliché. The killer needs motivation, a history, a background that MUST be exposed in some manner before the reveal)
Knox's 6th: It is forbidden for accident or intuition to be employed as a detective technique. (Bigby isn't going to solve the case by some lucky happenstance or by following a vision from heaven because that would mean he would have access to information that the reader does not, and CAN not, possess. Logic alone must be the key)
Knox's 7th: It is forbidden for the detective to be the culprit. (For Bigby to be the killer, it means he is hiding things from the audience, and therefore is not solvable in a fair way. It goes against everything Knox stands for)
Knox's 8th: It is forbidden for the case to be resolved with clues that are not presented. (a mystery must, MUST, be solvable by the reader before the true culprit is caught)
Knox's 9th: It is permitted for observers to let their own conclusions and interpretations be heard. (remember kids, everyone lies. If someone says they have an airtight alibi, that's probably a lie too. If you are told someone is dead without seeing it with your own eyes, there is a good chance they are alive instead. Trusting people is for saps, every person you meet is likely there to deceive you. There is only two things you can believe in. That is the evidence and the detective)
Knox's 10th: It is forbidden for a character to disguise themselves as another without any clues. (the killer can't disguise himself as, say, an innocent cab driver without leaving a clue to his true identity)
Does this game follow the rules? I do not know. Certainly, looking from episode 1, it appears to follow the rules. We've had 3 investigations so far. All have had clues splattered around the area so that the detective could make some conclusions. There is some problems with the death of Faith's husband, such as the gun issue but I think that was a slip up, not intentional by design.
To all new readers: While it is not conclusive that TellTale is following the Decalogue, there is sufficient evidence, for now, for it to be possible, perhaps probable. Therefore, all theories posted here should do one of two things, either prove one of the commandments has been broken in such a way that it proves that this is not a fair play detective story or craft a theory that doesn't conflict with them. There are plenty of threads where one can create devil's proof arguments. This is not one of them.